After releasing the grapple, you can move 15 more feet
Movement speed is only halved while you are dragging the creature
When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.
The condition is clear, when you move with a grappled creature your speed is halved. If you are no longer moving with a grappled creature, this rule no longer applies and your speed becomes normal.
When your speed changes, the amount you can move also changes
On your turn, you can move a distance up to your speed.
This is a simple rule and it has no qualifiers. During one round you can move up to whatever your current speed is. It doesn't mention any exceptions for cases where your speed might increase or decrease during the turn. So the rule simply is:
$$ movementLeft = currentSpeed - movementUsed $$
So, if your speed increases during your turn (for example if you cast haste on yourself), you can move further that round. If it decreases, so does the distance you can move.
Thus, if you move 15 feet with your grappled creature you have moved 15 feet with a speed of 15.
$$ movementLeft = 15 - 15 = 0 $$
After releasing the grapple, your speed becomes 30.
$$ movementLeft = 30 - 15 = 15 $$
And, according to the rules, you can move a distance up to your speed on your turn. Since you have already moved 15 and you have a speed of 30, you have 15 feet more you can go.
You cannot use the difficult terrain method for this movement
Conditions such a difficult terrain use very different rules and language for describing how movement is penalized.
Every foot of movement costs one extra foot
This is not how the moving a grappled creature rules are written at all and they aren't the same as this question demonstrates. Without language like this in the rule for grappled creatures, there is no rules support for calculating the movement the same way. It is also worth noting that haste and slow use the exact same wording, so whatever you rule here would apply to those as well.